what does this "gavel" part mean?
The Senator stared at him as though through a veil, then looked at Holland, who was deftly approaching from the other side to relieve him of the gavel. "How do you know?"】

what does "relieve him of the gavel" mean?

Question

what does this "gavel" part mean?
The Senator stared at him as though through a veil, then looked at Holland, who was deftly approaching from the other side to relieve him of the gavel. "How do you know?"】

what does "relieve him of the gavel" mean?

Answer

"To relieve (somebody) of (something)" means to take something from somebody.  Holland was moving to take the gavel, and effectively take away that person's authority to speak.

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